Problem020.js

/**
 * Problem 20 - Factorial digit sum
 *
 * @see {@link https://projecteuler.net/problem=20}
 *
 * n! means n × (n − 1) × ... × 3 × 2 × 1
 *
 * For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800,
 * and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27
 *
 * Find the sum of the digits in the number 100!
 */

const factorialDigitSum = (n = 100) => {
  // Consider each digit*10^exp separately, right-to-left ([units, tens, ...]).
  const digits = [1]

  for (let x = 2; x <= n; x++) {
    let carry = 0
    for (let exp = 0; exp < digits.length; exp++) {
      const prod = digits[exp] * x + carry
      carry = Math.floor(prod / 10)
      digits[exp] = prod % 10
    }
    while (carry > 0) {
      digits.push(carry % 10)
      carry = Math.floor(carry / 10)
    }
  }

  // (digits are reversed but we only want the sum so it doesn't matter)

  return digits.reduce((prev, current) => prev + current, 0)
}

export { factorialDigitSum }